On general nonlinear and quasilinear unanticipative feedback systems

Nonlinear Transmission Problems for Quasilinear Parabolic Systems

We study degenerate quasilinear parabolic systems in two different domains, which are connected by a nonlinear transmission condition at their interface. For a large class of models, including those modeling pollution aggression on stones and chemotactic movements of bacteria, we prove global existence, uniqueness and stability of the solutions.

Stability of extremum seeking feedback for general nonlinear dynamic systems

While the mainstream methods of adaptive control (both linear and nonlinear) deal only with regulation to known set points or reference trajectories, in many applications the set point should be selected to achieve a maximum of an uncertain reference-to-output equilibrium map. The techniques of the so-called `extremum controla or `self-optimizing controla developed for this problem in the 1950}...

Quasilinear Elliptic Systems of Resonant Type and Nonlinear Eigenvalue Problems

ON QUASILINEAR ELLIPTIC SYSTEMS INVOLVING MULTIPLE CRITICAL EXPONENTS

In this paper, we consider the existence of a non-trivial weaksolution to a quasilinear elliptic system involving critical Hardyexponents. The main issue of the paper is to understand thebehavior of these Palais-Smale sequences. Indeed, the principaldifficulty here is that there is an asymptotic competition betweenthe energy functional carried by the critical nonlinearities. Thenby the variatio...

On General Nonlinear Constrained Mechanical Systems

This paper develops a new, simple, general, and explicit form of the equations of motion for general constrained mechanical systems that can have holonomic and/or nonholonomic constraints that may or may not be ideal, and that may contain either positive semi-definite or positive definite mass matrices. This is done through the replacement of the actual unconstrained mechanical system, which ma...